**Summary:**

Another great investigative mathematics lesson that evolves from students playing a fun game. They have to calculate the chance and probability of rolling 2 dice and see which horse(s) has a greater chance at winning the game. Links to working with fractions, decimals and percentages.

**Australian Curriculum Links:**

- Year 5 – List outcomes of chance experiments involving equally likely outcomes and represent probabilities of those outcomes using fractions (ACMSP116)
- Year 5 – Recognise that probabilities range from 0 to 1 (ACMSP117)
- Year 6 – Describe probabilities using fractions, decimals and percentages (ACMSP144)
- Year 7 – Assign probabilities to the outcomes of events and determine probabilities for events (ACMSP168)

**Lesson Outline:**

Teacher notes:

This game works by having the children take turns in selecting horses (numbers 2-12) on the gameboard and then rolling the dice. Once the dice are rolled, add the score together and the total is the number of the horse that moves one space. The winning horse is the horse that reaches the bottom square the fastest.

Introduction:

- Introduce the game to the students by showing them the gameboard, discussing the rules and materials needed.
- Explain to the students that we are going to investigate the probability and chance of each horse winning this game and decide whether the game is fair or not.
- Ask ‘Who thinks they know the horse that will win?’ Then take responses on the board.
- Ask ‘How can we record what happens in our game?’ Then model how to collect raw data and how to draw a tally of wins.
- Set children off in pairs and allow them to play the game a few times.

Body:

- Once the children have some data, ask them to call out how many times each horse won and collate into a class tally/table.
- Ask them why they think a particular horse went quite well and why others did not.
- Now ask them how we, as mathematicians, can prove why some numbers have a better chance and probability than others.
- Have the children write down the numbers from 2-12 down the side of their page.
- Ask them to record the possibilities of reaching each number (e.g. 4 can be made with a 1 & 3, as well as a 2 & 2) You may like them to draw the dice (see below). Now set them off again.
- When finished ask the children to add up all of the chances that can occur (36). Then ask them to record each number as a fraction (e.g. 3 has 2/36 chances).
- Ask students how we convert a fraction to a decimal (if they are not sure, draw a square and halve it and explain that you had 1 thing and divided it into 2 parts (1/2)).
- Now do the same on a calculator (1 ÷ 2 = 0.5)
- Explain that it is the same with all fractions and that we can work out the decimal chance for number 3 by doing 2 ÷ 36 (0.055)
- Now make the link between the hundredths part of the decimal being the percentage (per – parts, cent – out of 100).
- For 0.055 that means it will be 6% (with rounding). Therefore the number 3 has a 6% chance of being rolled in this game.
- Workshop with children and allow them to continue investigating the percentage chance for the other numbers.

Conclusion:

- Once students have completed the task, ask them to add up the total percentages and see what they equal. Why might there be a variance if the whole is equal to 100% …?
- Ask the students to add up the total of all the decimal numbers. What does it equal? How is 1.0 and 100% the same?
- Finally ask the students to write a short response to ‘Is this game fair?’

**Assessment:**

- Anecdotal Notes
- Workbook Samples
- Written Response to ‘Is this game fair?’

**Resources:**

- Horse Racing Probability (DOC game)
- Counters (11 per pair 6 of one colour and 5 another colour)
- 2 Dice (per pair)